Maxwell's Electro-magnetic Theory of Light. 379 



Hence the magnitude of the displacement, necessary to account 

 for the dielectric properties of a medium possessing the highest 

 specific inductive capacity known, is small, even when compared with 

 molecular magnitudes. 



In determining the force acting 011 a charged atom within a 

 polarised dielectric, a difficulty arises somewhat similar to that expe- 

 rienced when the force on a magnetic molecule within a magnet is 

 sought.* The above method, I think, is not open to very serious 

 objection, and as the results obtained give a fair explanation of the 

 experimental facts, it may, perhaps, be tentatively adopted. 



[Added May 10. Mr. Larmorf gives P + f?rI as a first approxima- 

 tion to the value of the total electric field at a point within a polarized 

 dielectric, I denoting the intensity of electrification, or the electric 

 moment of the polarized medium per unit volume. As a consequence, 

 the Lorenz refraction equivalent is obtained, whilst the relation 

 (/i 2 I)oo density follows from the reasoning employed in the present 

 paper. Further, a dispersion formula, differing somewhat from that 

 of Ketteler, is obtained by Mr. Larmor ; it would be interesting to 

 know with what degree of accuracy this formula is capable of repre- 

 senting the dispersion of transparent substances, as determined, for 

 instance, by Paschen and Bubeiis.J 



The following somewhat simple argument is submitted in justifica- 

 tion of the assumption made above, that the field in a polarized 

 medium is equal to P. 



Let the space between two plane and parallel condenser plates, 

 separated by a distance small in comparison with the area of either, 

 be filled with an isotropic polarizable medium, such as that assumed 

 above. The molecules are assumed to be in a state of equilibrium 

 amongst themselves when the two plates are at the same potential ; 

 consequently the potential energy W, due to the small rotations 

 0i, 02, 03, .... of the several molecules composing the medium maybe 

 represented by a quadratic function of the form 



W = 



A similar expression would obtain for the potential energy due to 

 the separation of the atoms within the molecules. The conditions 

 connecting the various coefficients are such that W is essentially 

 positive. 



Considering for a moment only the molecular rotations, the force 



* See Maxwell's ' Electricity,' vol. 1, p. 83, 1892 edition, footnote by Professor 

 J. J. Thomson. 



f " A Dynamical Theory of the Electric and Luminiferous Medium, Part III," 

 ' Phil. Trans.,' A, vol. 190 (1897), 1821, pp. 232236. 



J Paschen, 'Wied. Ann.,' 1894, vol. 53, pp. 812822; Kubens, ' Wied. Ann.,' 

 1895, vol. 54, pp. 476485. 



